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Computational indistinguishability

In computational complexity, if \scriptstyle\{ D_n \}_{n \in \mathbb{N}} and \scriptstyle\{ E_n \}_{n \in \mathbb{N}} are two distribution ensembles indexed by a security parameter n, then we say they are computationally indistinguishable if for any nonuniform probabilistic polynomial time algorithm A, the following quantity is a negligible function in n:

\delta(n) = \left| \Pr_{x \gets D_n}[ A(x) = 1] - \Pr_{x \gets E_n}[ A(x) = 1] \right|.

In other words, for every efficient algorithm A, its behavior does not significantly change when given samples according to Dn or En.





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